LECTURE 1:
III. Four Arguments for Skepticism
I’ll consider just two of the arguments.
A. “The Possibility of Error Argument” [skip]
B. “The Indistinguishability Argument”
Point out pp. 116-7 and read the argument.
To set up this argument for skepticism, we need to put together several pieces.
First piece.
Consider the following two cases:
[WRITE ON BOARD]
(Case 1) Under normal conditions, a human subject S sees an oak tree in bright daylight and with an unobstructed view.
(Case 2) There are no oak trees anywhere nearby, but S’s human brain is stimulated by the machinery of an evil genius to have sensations just like those S would have if S saw an oak tree under normal conditions. [S is a ‘brain-in-a-vat.’]
These two cases are very different. However, from the point-of-view of the human subject in both of those cases, things look just as they would if he or she were really seeing an oak tree. That is, in both (Case 1) and (Case 2), a human subject would have experiences that are qualitatively identical.
What is introspective indistinguishability? Here are two plausible claims that explain somewhat (cases are conditions, as opposed to states of affairs):
[WRITE ON BOARD]
(II 1) Case A is introspectively indistinguishable from case B [for a subject S] iff, from S’s point-of-view, there is nothing about being in case A that differs from being in case B.
(II 2) Case A is introspectively indistinguishable from case B [for a subject S] iff being in case A seems just the same to S as being in case B.
Second piece.
Our experiences, memories and other introspectible mental states (at bottom) make up all the evidence we (humans) have. According to some theories of knowledge, the following is possible: Steve looks up and sees an oak tree outside his window. Steve remembers reading a book on tree identification and recalls the description of an oak tree. Steve notes the way the tree looks and, on the basis of his evidence, he comes to know that there is an oak tree.
Note that Steve might have had qualitatively identical evidence for there is an oak tree if he were a brain-in-a-vat – as in (Case 2) above. His evidence for there is an oak tree is fallible.
[WRITE ON BOARD]
(FE) S’s evidence E for P is fallible evidence iff: it is possible that both S has E and P is false.
Maybe some of our evidence for things we believe is not fallible in this way. But when we consider propositions that assert the existence of, or describe, contingently existing mind-independent objects, (nearly all?) the evidence we have is fallible.
This second piece of our discussion gives some reason to think premise (5-4) is true.
(5-4) But all the evidence we have for any propositions about the external world is fallible.
Third piece.
Suppose that one can have knowledge on the basis of fallible evidence. Then, let us focus on one such (alleged) case of knowledge – like the situation involving Steve seeing an oak tree. Imagine that we change Steve’s situation, while holding certain features fixed: Steve has experiences, (apparent) memories and such like those in the original example, but unlike the original case, there is no oak tree outside the window, or anywhere else nearby. Steve’s senses are being temporarily manipulated by an evil genius. That situation also seems possible. This reasoning suggests premise (5-1) is true.
(5-1) If a person can have knowledge on the basis of fallible evidence, then there can be cases of knowledge that are “introspectively indistinguishable” from cases of non-knowledge.
Fourth piece.
(5-1) and (5-4) are pretty clearly correct. (5-3) follows from (5-1) and (5-2). So, what about (5-2)?
(5-2) But there cannot be cases of knowledge that are introspectively indistinguishable from cases of non-knowledge.
“The Moorean Response” (pp. 121-2)
Note that the above argument entails that you do not know that you have hands. One response to this argument (as well as to others) is as follows: “Look, it is far more reasonable to believe that I know I have hands than it is to believe that all of the premises of this skeptical argument are true. So, I may reasonably reject the argument because at least one of the premises is mistaken.”
This response is okay, as far as it goes. But it is unsatisfying. If possible, we’d like to say what is wrong with the argument. In other words, we’d like to find out the mistake being made, if there is one.
Back on track…
Why think that (5-2) is true? Here’s one simple argument for (5-2):
[WRITE ON BOARD]
1. For any human subject S and proposition p, S can tell whether or not he knows p.
2. If (1) is true, then there cannot be cases of knowledge that are introspectively indistinguishable from cases of non-knowledge.
3. There cannot be cases of knowledge that are introspectively indistinguishable from cases of non-knowledge. [By deduction from (1) and (2).]
Premise (1) is extremely implausible. Consider the proposition that I am not having very vivid hallucinations. Premise (1) entails I can tell whether or not I know that I am not having very vivid hallucinations. And it also entails that I can tell whether or not I know that I can tell whether or not I know that I am not having very vivid hallucinations… and so on, ad infinitum. It seems that, at some point, we can get an example of a proposition that I am just not able to tell whether or not I know it is so.
Perhaps we have missed some considerations that support (5-2), but it is still worth pointing out that the main argument for skepticism considered rests on at least one problematic premise.
C. “The Certainty Argument”
Review the argument in the text.
Distinguish different senses of “certainty.”
Psychological certainty
[WRITE ON BOARD]
S is absolutely certain of p iff the strength of S’s conviction that p is maximal.
Epistemic certainty
[WRITE ON BOARD]
S is absolutely certain of p iff the strength of S’s reasons/evidence for p is maximal.
Restate the argument with “certainty” disambiguated.
Disambiguation 1 – certainty as psychological certainty
(6-1P) If S knows p, then the strength of S’s conviction that p is maximal.
(6-2P) It is not the case that the strength of any one’s conviction about an ‘external-world’ proposition is maximal.
(6-3) It is not the case that any one knows any ‘external-world’ proposition.
Neither (6-1P) nor (6-2P) are plausible. Consider the following examples:
(Example 1) Leonard is a competent mathematician, but he is prone to doubt himself, perhaps because of his upbringing. Leonard formulates a proof of a proposition p. His proof is sound and he has no good reason to doubt his conclusion. Lastly, although he believes p, he doesn’t have utter confidence in his conclusion.
(Evaluation of Example 1) Leonard knows p but the strength of Leonard’s conviction that p is not maximal. So, (6-1P) is false.
(Example 2) Joe tends to be overly confident in the things he believes. In particular, Joe believes that there are other human beings and the strength of his conviction is maximal. Joe is not unlike ordinary people in this respect.
(Evaluation of Example 2) Like Joe, the strength of some people’s conviction that there are other human beings is maximal. So, (6-2P) is false.
So, this argument does not provide adequate reason to believe (6-3).
Disambiguation 2 – certainty as epistemic certainty
(6-1E) If S knows p, then the strength of S’s reasons/evidence for p is maximal.
(6-2E) It is not the case that the strength of any one’s reasons/evidence for an ‘external-world’ proposition is maximal.
(6-3) It is not the case that any one knows any ‘external-world’ proposition.
The second argument for (6-3) is much more promising than the first.
Let’s consider an argument for (6-1E) that makes use of more plausible assumptions:
[WRITE ON BOARD]
(1) If it is not the case that the strength of S’s reasons/evidence for p is maximal then it is not the case that S’s evidence rules out every possibility in which not-p.
(2) If it is not the case that S’s evidence rules out every possibility in which not-p then it is not the case that S knows p.
(3) If it is not the case that the strength of S’s reasons/evidence for p is maximal then it is not the case that S knows p. [By deduction from (1) and (2).]
(4) If S knows p then the strength of S’s reasons/evidence for p is maximal. [By contraposition of (3).]
Notice that (4) and (6-1E) say the same thing.
Doubt creeps in when we think about what it is for someone’s evidence to rule out a possibility. Here are some candidate explanations of “ruling out a possibility.”
[WRITE ON BOARD]
(RULE 1) S’s evidence rules out a possibility in which p iff S’s evidence makes believing not-p reasonable.
(RULE 2) S’s evidence rules out a possibility in which p iff S knows not-p on the basis of S’s evidence.
Either one of these candidate explanations gives rise to a problem.
(1-RULE 1) If it is not the case that the strength of S’s reasons/evidence for p is maximal then it is not the case that S’s evidence makes believing p reasonable.
(1-RULE 1) does not seem at all plausible.
(1-RULE 2) If it is not the case that the strength of S’s reasons/evidence for p is maximal then it is not the case that S knows p on the basis of S’s evidence.
(1-RULE 2) is equivalent to (4) and (6-1E). So, even if (1-RULE 2) is true, our sub-argument (under this interpretation) lends no insight.
D. “The Transmissibility Argument” [skip]
IV. Responding to Skepticism
A. The Skeptical View is Self-refuting [skip]
B. The Moorean Response [already stated]
C. Fallibilism
C1. Knowledge and Absolute Certainty
This argument for skepticism assumes that knowledge imposes extremely high standards. On the contrary, according to fallibilism, knowing p requires having good/strong reasons/evidence for p, but it does not require “infallible” or maximally strong evidence for p. In other words, fallibilists say it is possible to know something while having evidence that does not guarantee the truth of the thing known.
If fallibilism is correct, then (6-1) of the “Certainty” argument is false.
C2. [Skip]
C3. The Introspective Indistinguishability Argument
This argument assumed that there cannot be case of knowledge that are introspectively indistinguishable from cases of non-nonknowledge. That was (5-2). But, if fallibilism is true, then (5-2) is false.
[The following argument is basically a re-statement of the argument I gave in class for premise (5-1) of the same argument.]
Suppose that fallibilism is true. Then it is possible that a subject S knows a proposition p while having reasons/evidence for p that are fallible and that do not make p absolutely certain. Consider one such possibility – in which Steve knows that there is an oak tree with fallible evidence. Then there is another possibility in which everything seems to Steve as it did in the first possibility, but Steve isn’t really perceiving an oak tree, there are no oak trees and Steve does not know that there is an oak tree.
But why think that fallibilism is true?
Two lines of reasoning support fallibilism.
First, we may consider the many examples that are consistent with fallibilism (and suggest that its denial is false). The example of normal Steve above seems to be a situation in which a person knows something while having only fallible evidence for what he knows. Likewise, nearly all cases of (alleged) perceptual knowledge suggest that fallibilism is true.
Second, we may consider cases where English speakers say things that appear to us to be true and which harmonize with fallibilism.
A: Do you know that you closed the door as we went out?
B: Yes.
A: Do you know with absolute certainty?
B: No, but I know I did.
This kind of dialogue is admittedly somewhat uncommon. But one can consistently suppose that B speaks truly in some such situation. If so, then that is a reason to think that knowledge does not entail knowing with maximal (epistemic) certainty.
LECTURE 2:
I. The Problem of Induction
We constantly draw conclusions on the basis of our experiences and memories and so forth. Sometimes, we draw conclusions about the make-up of a group that we haven’t exhaustively examined. Consider the following typical argument:
[WRITE ON BOARD]
45 of 55 [randomly] sampled Swedes [with respect to being Protestant] are Protestant
=== with 95% probability ===
76-86% of Swedes are Protestant
In addition, we occasionally use assumptions about the rough make-up of a group to draw conclusions about unexamined members. In addition to the above typical argument, we have another:
[WRITE ON BOARD]
81% of Swedes are Protestant
Petersen is a [random] Swede [with respect to being Protestant]
=== with 81% probability ===
Petersen is Protestant
The same reasoning is used in scientific investigation – although these investigations are often held to a higher standard of rigor and thoroughness than ordinary thinking.
We may note three things to about this “inductive” reasoning.
First. The reasoning we employ seems to be different than purely mathematical or deductive reasoning.
Second. Frequently, something about inductive reasoning gives one justification to believe things about the world. Of course, there are cases where such reasoning does not provide justification.
Third. It is not easy to understand this reasoning. One reason for this is that, unlike the case of deductive/mathematical arguments, it seems to be extremely difficult (if not impossible) to state what “good patterns of inductive reasoning” are. Another reason is that there is quite a bit of disagreement about what role such reasoning plays in acquiring justification or knowledge (if it does so at all).
David Hume famously argued that humans do not have knowledge except of their own ideas. When it comes to inductive reasoning – or what Hume called “moral argument” or “probable reasoning” – Hume claimed that such inductive reasoning never provides reasons for believing its conclusions. Instead, according to Hume, we believe these inductive conclusions purely as a result of intellectual habit.
We aren’t going to try to interpret Hume’s philosophical writing. But, in order to appreciate the argument we associate with him, we have to understand a few things.
First, premise (5-5) says that all moral arguments assume that nature is “uniform” in some sense. In other words, if one does not have justification to believe that nature has a certain sort of regularity, then, for example, one’s experiences of past sunrises do not provide one with good reasons to believe that the sun will rise tomorrow.
As it turns out, it is hard to spell out what kind of “uniformity of nature” claim is presupposed by inductive reasoning. Here are some possibilities given in our text:
[WRITE ON THE BOARD]
(PF) If X percent of the observed As have been Bs then X percent of the unobserved As are Bs. [‘The future will be like the past.’
Second, premise (5-1) says that if the principle of “the uniformity of nature” can be justified at all, then it can be justified by one of two kinds of argument: a demonstrative argument or a moral argument.
Standard demonstrative arguments include those deductive arguments seen in mathematical proofs: the premises are known necessary truths and the conclusions follow of necessity.
Standard moral arguments might include our examples above, as well as the numbered arguments on pp. 131-2 of the text.
Third, the argument assumes that (PF) is not a necessary truth. At best, it is contingently true.
Read “Hume’s Argument” slowly (p. 134) and instruct students to append the following lines to it in their notes:
[WRITE ON BOARD]
(5-10) If (PF) cannot be justified then it is not the case that anyone has epistemic justification to believe the conclusion of an inductive argument.
(5-11) It is not the case that anyone has epistemic justification to believe the conclusion of an inductive argument. [By deduction from (5-9) and (5-10).]
Like the original argument (5-1) – (5-9), the extended argument (5-1) – (5-11) is valid. (5-11) utterly disagrees with common sense and the considered views of many philosophers and scientists. What gives?
Reply 1: Deny (5-1) – Sometimes a person is justified in believing something without having an argument for it. Consider the proposition that your head aches or that two is greater than one. Of course, there are arguments for these propositions, but it seems one may know them without having any argument.
Reply to Reply 1: However, maybe the “uniformity of nature” principle isn’t like that.
Reply 2: Deny (5-3) – (PF) is necessary.
Reply to Reply 2: (PF) is plainly not necessarily true. (It doesn’t even seem to be true!) There is no contradiction in assuming that, up until now, massive bodies have always fallen to earth when released, but tomorrow those massive bodies will be repelled in the same circumstances.
Reply 3: Deny (5-5) – The arguments we’ve seen do not explicitly say anything about “uniformity” or “nature” or “the uniformity of nature.” The “uniformity of nature” is not relevant to the rationality of induction.
Reply to Reply 3: True, the arguments we’ve considered don’t have the uniformity of nature as a premise (or part of a premise). But, if nature weren’t in some sense “regular” or “uniform” then what license do we have to infer things about unobserved things on the basis of what we observe?
Reply 4: Deny (5-7) – Some circular arguments prove their conclusions. For example: There are circular arguments, so there are circular arguments.
Reply to Reply 4: That’s a cute trick. However, your example doesn’t prove there are circular arguments – it is a circular argument. We know that there are circular arguments by considering the example, but not because the conclusion is supported by the premise. Anyway, the sort of circularity was this:
[WRITE ON BOARD]
(PF) has been correct in the past. So, it will be true in the future.
And that is plainly not persuasive. We are in doubt about (PF), so how could that argument (or anything like it) suffice to give us a good reason’s for (PF)?
Reply 5: Deny (5-10) –
Notice that the slogan ‘The future will be like the past’ does not specify in what respects the future will be like the past. But, of course, the future will not be like the past in every respect. At one time in the past, I was 5 years old. At no time in the future will I be 5 years old. Nor does it seem to be precise enough to explain the standards we apply to inductive reasoning, as with our sample inductive arguments above.
Taken as a perfectly general claim, (PF) is false. Suppose I take a particular quarter and begin flipping it. On the first flip, the result is “heads.” At this point, we can infer from (PF) that, since 100% of the observed flips of this coin have been “heads”, 100% of the unobserved flips of this coin are (will be) “heads.” Well, suppose I continue flipping that quarter – surely it is possible that in the next several flips I get “tails.” When I get the result “tails,” I destroy the coin (so there are no more flips of that coin). If so, then (PF) is false.
So (PF) is false. Where does that leave us? While it may be that our justification to believe inductive conclusions depends on something other than the explicitly given premises of inductive arguments (like the ones we’ve considered), it seems that the other thing is not (PF).
First, (PF) does not require that we have any particular relationship to the premises of an inductive argument in order to have justification to believe its conclusion.
Second, (PF) does not allow further information to undermine or bolster one’s inductive conclusions.
[WRITE ON BOARD]
45 of 55 observed Swedes are Protestant.
===
76-86% [‘roughly 81%’] of Swedes are Protestant.
[WRITE ON BOARD]
45 of 55 observed Swedes are Protestant.
All of the observed Swedes were approached on Sunday morning within 50 feet of a Protestant church.
There are many Roman Catholic churches surrounding the Protestant church visited.
===
76-86% [‘roughly 81%’] of Swedes are Protestant.
Clearly, the first argument presents a decent case for the conclusion – the second adds more information and that makes the conclusion far less plausible. But this fact doesn’t fit with what is implied by (PF).
[WRITE ON BOARD]
(PFR) Knowing that things have been a certain way in the past gives you a good [but not conclusive] reason to believe that they will be that way in the future.
What role does (PFR) play in the justification of inductive conclusions? I want to contrast two ideas:
[WRITE ON BOARD]
(SUN 1) In order for your observations of past sunrises to give you a reason to believe that the sun will rise the next day, you must know that (PFR) is true.
(SUN 2) In order for your observations of past sunrises to give you a reason to believe that the sun will rise the next day, (PFR) must be true.
I am proposing that (SUN 2) is true. By contrast, (SUN 1) may not correctly apply to everyone.
Unlike (PF), (PFR) is (plausibly) a necessary truth that we can defend by appeal to examples of “good inductive reasoning”:
[WRITE ON BOARD]
If S knows that 45 of 55 [randomly] sampled Swedes [with respect to being Protestant] are Protestant then that gives S a good (though not conclusive) reason to believe that [‘roughly 81%’] of Swedes are Protestant.
IV. Responding to Skepticism
A. The Skeptical View is Self-refuting [skip]
B. The Moorean Response [already stated]
C. Fallibilism
C1. Knowledge and Absolute Certainty
This argument for skepticism assumes that knowledge imposes extremely high standards. On the contrary, according to fallibilism, knowing p requires having good/strong reasons/evidence for p, but it does not require “infallible” or maximally strong evidence for p. In other words, fallibilists say it is possible to know something while having evidence that does not guarantee the truth of the thing known.
If fallibilism is correct, then (6-1) of the “Certainty” argument is false.
C2. [Skip]
C3. The Introspective Indistinguishability Argument
This argument assumed that there cannot be case of knowledge that are introspectively indistinguishable from cases of non-nonknowledge. That was (5-2). But, if fallibilism is true, then (5-2) is false.
[The following argument is basically a re-statement of the argument I gave in class for premise (5-1) of the same argument.]
Suppose that fallibilism is true. Then it is possible that a subject S knows a proposition p while having reasons/evidence for p that are fallible and that do not make p absolutely certain. Consider one such possibility – in which Steve knows that there is an oak tree with fallible evidence. Then there is another possibility in which everything seems to Steve as it did in the first possibility, but Steve isn’t really perceiving an oak tree, there are no oak trees and Steve does not know that there is an oak tree.
But why think that fallibilism is true?
Two lines of reasoning support fallibilism.
First, we may consider the many examples that are consistent with fallibilism (and suggest that its denial is false). The example of normal Steve above seems to be a situation in which a person knows something while having only fallible evidence for what he knows. Likewise, nearly all cases of (alleged) perceptual knowledge suggest that fallibilism is true.
Second, we may consider cases where English speakers say things that appear to us to be true and which harmonize with fallibilism.
A: Do you know that you closed the door as we went out?
B: Yes.
A: Do you know with absolute certainty?
B: No, but I know I did.
This kind of dialogue is admittedly somewhat uncommon. But one can consistently suppose that B speaks truly in some such situation. If so, then that is a reason to think that knowledge does not entail knowing with maximal (epistemic) certainty.
LECTURE 2:
I. The Problem of Induction
We constantly draw conclusions on the basis of our experiences and memories and so forth. Sometimes, we draw conclusions about the make-up of a group that we haven’t exhaustively examined. Consider the following typical argument:
[WRITE ON BOARD]
45 of 55 [randomly] sampled Swedes [with respect to being Protestant] are Protestant
=== with 95% probability ===
76-86% of Swedes are Protestant
In addition, we occasionally use assumptions about the rough make-up of a group to draw conclusions about unexamined members. In addition to the above typical argument, we have another:
[WRITE ON BOARD]
81% of Swedes are Protestant
Petersen is a [random] Swede [with respect to being Protestant]
=== with 81% probability ===
Petersen is Protestant
The same reasoning is used in scientific investigation – although these investigations are often held to a higher standard of rigor and thoroughness than ordinary thinking.
We may note three things to about this “inductive” reasoning.
First. The reasoning we employ seems to be different than purely mathematical or deductive reasoning.
Second. Frequently, something about inductive reasoning gives one justification to believe things about the world. Of course, there are cases where such reasoning does not provide justification.
Third. It is not easy to understand this reasoning. One reason for this is that, unlike the case of deductive/mathematical arguments, it seems to be extremely difficult (if not impossible) to state what “good patterns of inductive reasoning” are. Another reason is that there is quite a bit of disagreement about what role such reasoning plays in acquiring justification or knowledge (if it does so at all).
David Hume famously argued that humans do not have knowledge except of their own ideas. When it comes to inductive reasoning – or what Hume called “moral argument” or “probable reasoning” – Hume claimed that such inductive reasoning never provides reasons for believing its conclusions. Instead, according to Hume, we believe these inductive conclusions purely as a result of intellectual habit.
We aren’t going to try to interpret Hume’s philosophical writing. But, in order to appreciate the argument we associate with him, we have to understand a few things.
First, premise (5-5) says that all moral arguments assume that nature is “uniform” in some sense. In other words, if one does not have justification to believe that nature has a certain sort of regularity, then, for example, one’s experiences of past sunrises do not provide one with good reasons to believe that the sun will rise tomorrow.
As it turns out, it is hard to spell out what kind of “uniformity of nature” claim is presupposed by inductive reasoning. Here are some possibilities given in our text:
[WRITE ON THE BOARD]
(PF) If X percent of the observed As have been Bs then X percent of the unobserved As are Bs. [‘The future will be like the past.’
Second, premise (5-1) says that if the principle of “the uniformity of nature” can be justified at all, then it can be justified by one of two kinds of argument: a demonstrative argument or a moral argument.
Standard demonstrative arguments include those deductive arguments seen in mathematical proofs: the premises are known necessary truths and the conclusions follow of necessity.
Standard moral arguments might include our examples above, as well as the numbered arguments on pp. 131-2 of the text.
Third, the argument assumes that (PF) is not a necessary truth. At best, it is contingently true.
Read “Hume’s Argument” slowly (p. 134) and instruct students to append the following lines to it in their notes:
[WRITE ON BOARD]
(5-10) If (PF) cannot be justified then it is not the case that anyone has epistemic justification to believe the conclusion of an inductive argument.
(5-11) It is not the case that anyone has epistemic justification to believe the conclusion of an inductive argument. [By deduction from (5-9) and (5-10).]
Like the original argument (5-1) – (5-9), the extended argument (5-1) – (5-11) is valid. (5-11) utterly disagrees with common sense and the considered views of many philosophers and scientists. What gives?
Reply 1: Deny (5-1) – Sometimes a person is justified in believing something without having an argument for it. Consider the proposition that your head aches or that two is greater than one. Of course, there are arguments for these propositions, but it seems one may know them without having any argument.
Reply to Reply 1: However, maybe the “uniformity of nature” principle isn’t like that.
Reply 2: Deny (5-3) – (PF) is necessary.
Reply to Reply 2: (PF) is plainly not necessarily true. (It doesn’t even seem to be true!) There is no contradiction in assuming that, up until now, massive bodies have always fallen to earth when released, but tomorrow those massive bodies will be repelled in the same circumstances.
Reply 3: Deny (5-5) – The arguments we’ve seen do not explicitly say anything about “uniformity” or “nature” or “the uniformity of nature.” The “uniformity of nature” is not relevant to the rationality of induction.
Reply to Reply 3: True, the arguments we’ve considered don’t have the uniformity of nature as a premise (or part of a premise). But, if nature weren’t in some sense “regular” or “uniform” then what license do we have to infer things about unobserved things on the basis of what we observe?
Reply 4: Deny (5-7) – Some circular arguments prove their conclusions. For example: There are circular arguments, so there are circular arguments.
Reply to Reply 4: That’s a cute trick. However, your example doesn’t prove there are circular arguments – it is a circular argument. We know that there are circular arguments by considering the example, but not because the conclusion is supported by the premise. Anyway, the sort of circularity was this:
[WRITE ON BOARD]
(PF) has been correct in the past. So, it will be true in the future.
And that is plainly not persuasive. We are in doubt about (PF), so how could that argument (or anything like it) suffice to give us a good reason’s for (PF)?
Reply 5: Deny (5-10) –
Notice that the slogan ‘The future will be like the past’ does not specify in what respects the future will be like the past. But, of course, the future will not be like the past in every respect. At one time in the past, I was 5 years old. At no time in the future will I be 5 years old. Nor does it seem to be precise enough to explain the standards we apply to inductive reasoning, as with our sample inductive arguments above.
Taken as a perfectly general claim, (PF) is false. Suppose I take a particular quarter and begin flipping it. On the first flip, the result is “heads.” At this point, we can infer from (PF) that, since 100% of the observed flips of this coin have been “heads”, 100% of the unobserved flips of this coin are (will be) “heads.” Well, suppose I continue flipping that quarter – surely it is possible that in the next several flips I get “tails.” When I get the result “tails,” I destroy the coin (so there are no more flips of that coin). If so, then (PF) is false.
So (PF) is false. Where does that leave us? While it may be that our justification to believe inductive conclusions depends on something other than the explicitly given premises of inductive arguments (like the ones we’ve considered), it seems that the other thing is not (PF).
First, (PF) does not require that we have any particular relationship to the premises of an inductive argument in order to have justification to believe its conclusion.
Second, (PF) does not allow further information to undermine or bolster one’s inductive conclusions.
[WRITE ON BOARD]
45 of 55 observed Swedes are Protestant.
===
76-86% [‘roughly 81%’] of Swedes are Protestant.
[WRITE ON BOARD]
45 of 55 observed Swedes are Protestant.
All of the observed Swedes were approached on Sunday morning within 50 feet of a Protestant church.
There are many Roman Catholic churches surrounding the Protestant church visited.
===
76-86% [‘roughly 81%’] of Swedes are Protestant.
Clearly, the first argument presents a decent case for the conclusion – the second adds more information and that makes the conclusion far less plausible. But this fact doesn’t fit with what is implied by (PF).
[WRITE ON BOARD]
(PFR) Knowing that things have been a certain way in the past gives you a good [but not conclusive] reason to believe that they will be that way in the future.
What role does (PFR) play in the justification of inductive conclusions? I want to contrast two ideas:
[WRITE ON BOARD]
(SUN 1) In order for your observations of past sunrises to give you a reason to believe that the sun will rise the next day, you must know that (PFR) is true.
(SUN 2) In order for your observations of past sunrises to give you a reason to believe that the sun will rise the next day, (PFR) must be true.
I am proposing that (SUN 2) is true. By contrast, (SUN 1) may not correctly apply to everyone.
Unlike (PF), (PFR) is (plausibly) a necessary truth that we can defend by appeal to examples of “good inductive reasoning”:
[WRITE ON BOARD]
If S knows that 45 of 55 [randomly] sampled Swedes [with respect to being Protestant] are Protestant then that gives S a good (though not conclusive) reason to believe that [‘roughly 81%’] of Swedes are Protestant.